Functions of Complex Variable

Fourier series: periodic functions, Fourier coefficients, functions of the
period 2pi, functions of the period T, even and odd functions, half - range
cosine and sine series, convergence of Fourier series. Functions of a complex
variable: complex numbers, complex functions of a real variable, Fourier series
at a complex form, complex functions of a complex variable and mappings,
complex differentiation, Cauchy - Riemann equations, complex series, Taylor and
Laurent series, singularities, zeros and residues, integration Cauchy theorem.